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Author : I. M. Glazman
Publisher : Courier Corporation
Page : 548 pages
File Size : 17,10 MB
Release : 2006-01-01
Category : Mathematics
ISBN : 0486453324
A sequence of 2,400 propositions and problems features only hints. Suitable for advanced undergraduates and graduate students, this unique approach encourages students to work out their own proofs. 1974 edition.
Author : Израиль Маркович Глазман
Publisher : MIT Press (MA)
Page : 520 pages
File Size : 26,47 MB
Release : 1974
Category : Algebras, Linear
ISBN : 9780262070584
First published in Russian in 1969, this remarkable book develops the subject of linear algebra in a novel fashion: it presents a logically interconnected sequence of propositions and problems--some 2400 in all--"without proofs" but with a scaffolding of hints and pointers. The student is asked to work out formal proofs systematically, proceeding from simple verifications to relatively advanced strategies and techniques of proof. The material is organized into ten chapters.The authors have based their approach on the fundamental pedagogic proposition that the best way to learn mathematics is to "do" mathematics-- that the essence of understanding any given set of mathematical propositions comes when the student succeeds in proving them for himself, however roughly, rather than after a mere reading of a series of proofs, however polished. This aspect of the book will appeal to strongly motivated students: it can be used as a resource for independent study and in cooperative seminars, preferably without faculty presence. Of course, it can also be used as the basis of more conventional lecture presentations. It is suggested that the book be introduced at the senior or the first-year graduate level.The book is also meant to give insight into functional analysis, which may be formulated as linear analysis within an infinite-dimensional framework. As the student allows his consideration of the propositions move toward the limiting case of unrestricted dimensionality, he will find that his conceptual outlook approaches that proper to functional analysis. In that regard, the book represents an introduction to the latter subject, free of the difficulties inherent in the explicit admission of infinities.
Author : Roger W. Brockett
Publisher : SIAM
Page : 260 pages
File Size : 11,71 MB
Release : 2015-05-26
Category : Mathematics
ISBN : 1611973872
Originally published in 1970, Finite Dimensional Linear Systems is a classic textbook that provides a solid foundation for learning about dynamical systems and encourages students to develop a reliable intuition for problem solving. The theory of linear systems has been the bedrock of control theory for 50 years and has served as the springboard for many significant developments, all the while remaining impervious to change. Since linearity lies at the heart of much of the mathematical analysis used in applications, a firm grounding in its central ideas is essential. This book touches upon many of the standard topics in applied mathematics, develops the theory of linear systems in a systematic way, making as much use as possible of vector ideas, and contains a number of nontrivial examples and many exercises.
Author : Mark S. Gockenbach
Publisher : CRC Press
Page : 674 pages
File Size : 10,34 MB
Release : 2011-06-15
Category : Mathematics
ISBN : 143981564X
Linear algebra forms the basis for much of modern mathematics—theoretical, applied, and computational. Finite-Dimensional Linear Algebra provides a solid foundation for the study of advanced mathematics and discusses applications of linear algebra to such diverse areas as combinatorics, differential equations, optimization, and approximation. The author begins with an overview of the essential themes of the book: linear equations, best approximation, and diagonalization. He then takes students through an axiomatic development of vector spaces, linear operators, eigenvalues, norms, and inner products. In addition to discussing the special properties of symmetric matrices, he covers the Jordan canonical form, an important theoretical tool, and the singular value decomposition, a powerful tool for computation. The final chapters present introductions to numerical linear algebra and analysis in vector spaces, including a brief introduction to functional analysis (infinite-dimensional linear algebra). Drawing on material from the author’s own course, this textbook gives students a strong theoretical understanding of linear algebra. It offers many illustrations of how linear algebra is used throughout mathematics.
Author : Glazman I M & Ljubic J.
Publisher :
Page : pages
File Size : 49,66 MB
Release : 1974
Category :
ISBN :
Author : Paul R. Halmos
Publisher : Courier Dover Publications
Page : 209 pages
File Size : 26,40 MB
Release : 2017-05-24
Category : Mathematics
ISBN : 0486822265
Classic, widely cited, and accessible treatment offers an ideal supplement to many traditional linear algebra texts. "Extremely well-written and logical, with short and elegant proofs." — MAA Reviews. 1958 edition.
Author : Bila Bollobás
Publisher : Cambridge University Press
Page : 256 pages
File Size : 44,33 MB
Release : 1990-11-29
Category : Mathematics
ISBN : 9780521383011
This introduction to functional analysis is intended for advanced undergraduate students, typically final year, who have some background in real analysis. The author's aim is not to cover the standard material in a standard way, but to present results of applications in contemporary mathematics and to show the relevance of functional analysis to other areas. Unusual topics covered include geometry of finite-dimensional spaces, invariant subspace, fixed-point theorem, and the Bishop-Phelps theorem. An outstanding set of exercises run from the elementary to the challenging.
Author : Bryan Rynne
Publisher : Springer Science & Business Media
Page : 276 pages
File Size : 19,29 MB
Release : 2013-03-14
Category : Mathematics
ISBN : 1447136551
This book provides an introduction to the ideas and methods of linear func tional analysis at a level appropriate to the final year of an undergraduate course at a British university. The prerequisites for reading it are a standard undergraduate knowledge of linear algebra and real analysis (including the the ory of metric spaces). Part of the development of functional analysis can be traced to attempts to find a suitable framework in which to discuss differential and integral equa tions. Often, the appropriate setting turned out to be a vector space of real or complex-valued functions defined on some set. In general, such a vector space is infinite-dimensional. This leads to difficulties in that, although many of the elementary properties of finite-dimensional vector spaces hold in infinite dimensional vector spaces, many others do not. For example, in general infinite dimensional vector spaces there is no framework in which to make sense of an alytic concepts such as convergence and continuity. Nevertheless, on the spaces of most interest to us there is often a norm (which extends the idea of the length of a vector to a somewhat more abstract setting). Since a norm on a vector space gives rise to a metric on the space, it is now possible to do analysis in the space. As real or complex-valued functions are often called functionals, the term functional analysis came to be used for this topic. We now briefly outline the contents of the book.
Author : Ioannis Koutromanos
Publisher : John Wiley & Sons
Page : 724 pages
File Size : 50,9 MB
Release : 2018-02-12
Category : Technology & Engineering
ISBN : 1119260086
An introductory textbook covering the fundamentals of linear finite element analysis (FEA) This book constitutes the first volume in a two-volume set that introduces readers to the theoretical foundations and the implementation of the finite element method (FEM). The first volume focuses on the use of the method for linear problems. A general procedure is presented for the finite element analysis (FEA) of a physical problem, where the goal is to specify the values of a field function. First, the strong form of the problem (governing differential equations and boundary conditions) is formulated. Subsequently, a weak form of the governing equations is established. Finally, a finite element approximation is introduced, transforming the weak form into a system of equations where the only unknowns are nodal values of the field function. The procedure is applied to one-dimensional elasticity and heat conduction, multi-dimensional steady-state scalar field problems (heat conduction, chemical diffusion, flow in porous media), multi-dimensional elasticity and structural mechanics (beams/shells), as well as time-dependent (dynamic) scalar field problems, elastodynamics and structural dynamics. Important concepts for finite element computations, such as isoparametric elements for multi-dimensional analysis and Gaussian quadrature for numerical evaluation of integrals, are presented and explained. Practical aspects of FEA and advanced topics, such as reduced integration procedures, mixed finite elements and verification and validation of the FEM are also discussed. Provides detailed derivations of finite element equations for a variety of problems. Incorporates quantitative examples on one-dimensional and multi-dimensional FEA. Provides an overview of multi-dimensional linear elasticity (definition of stress and strain tensors, coordinate transformation rules, stress-strain relation and material symmetry) before presenting the pertinent FEA procedures. Discusses practical and advanced aspects of FEA, such as treatment of constraints, locking, reduced integration, hourglass control, and multi-field (mixed) formulations. Includes chapters on transient (step-by-step) solution schemes for time-dependent scalar field problems and elastodynamics/structural dynamics. Contains a chapter dedicated to verification and validation for the FEM and another chapter dedicated to solution of linear systems of equations and to introductory notions of parallel computing. Includes appendices with a review of matrix algebra and overview of matrix analysis of discrete systems. Accompanied by a website hosting an open-source finite element program for linear elasticity and heat conduction, together with a user tutorial. Fundamentals of Finite Element Analysis: Linear Finite Element Analysis is an ideal text for undergraduate and graduate students in civil, aerospace and mechanical engineering, finite element software vendors, as well as practicing engineers and anybody with an interest in linear finite element analysis.
Author : Michael I. Gil'
Publisher : Springer Science & Business Media
Page : 386 pages
File Size : 39,65 MB
Release : 1998-09-30
Category : Mathematics
ISBN : 9780792382218
The aim of Stability of Finite and Infinite Dimensional Systems is to provide new tools for specialists in control system theory, stability theory of ordinary and partial differential equations, and differential-delay equations. Stability of Finite and Infinite Dimensional Systems is the first book that gives a systematic exposition of the approach to stability analysis which is based on estimates for matrix-valued and operator-valued functions, allowing us to investigate various classes of finite and infinite dimensional systems from the unified viewpoint. This book contains solutions to the problems connected with the Aizerman and generalized Aizerman conjectures and presents fundamental results by A. Yu. Levin for the stability of nonautonomous systems having variable real characteristic roots. Stability of Finite and Infinite Dimensional Systems is intended not only for specialists in stability theory, but for anyone interested in various applications who has had at least a first-year graduate-level course in analysis.